| 引用本文: | 常浩,王春峰,房振明.随机金融市场环境下的最优再保险–投资策略[J].控制理论与应用,2019,36(2):307~318.[点击复制] |
| CHANG Hao,WANG Chun-feng,FANG Zhen-ming.Optimal reinsurance-investment strategy in a stochastic financial market[J].Control Theory and Technology,2019,36(2):307~318.[点击复制] |
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| 随机金融市场环境下的最优再保险–投资策略 |
| Optimal reinsurance-investment strategy in a stochastic financial market |
| 摘要点击 2387 全文点击 999 投稿时间：2017-11-06 修订日期：2018-05-24 |
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| DOI编号 10.7641/CTA.2018.70807 |
| 2019,36(2):307-318 |
| 中文关键词 仿射利率模型 Heston模型 指数效用 最优控制理论 最优再保险-投资策略 |
| 英文关键词 Affine interest rate model Heston model exponential utility optimal control theory optimal reinsurance-investment strategy |
| 基金项目 国家自然科学基金面上项目(批准号：71671122)，中国博士后科学基金(批准号: 2014M560185, 2016T90203)，教育部人文社会科学研究基金规划项目(批准号:16YJA790004)，天津市自然科学基金(批准号: 15JCQNJC04000). |
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| 中文摘要 |
| 为了对冲保险风险，保险公司可以向再保险公司购买比例再保险. 为了保值增值，保险公司可以将其财富投资于金融市场. 假设盈余过程由带漂移的布朗运动所驱动，利率满足仿射利率模型，股票波动率满足Heston随机波动率模型. 应用随机最优控制和HJB方程方法，我们得到了指数效用下最优再保险-投资策略的显式解. 通过数值算例，我们分析了模型参数对最优再保险策略和最优投资策略的影响. 研究结果表明：最优再保险策略不仅依赖于保险市场参数，而且依赖于金融市场参数；随机利率与随机波动率模型下的最优再保险-投资策略与利率动态密切相关，而与波动率动态无关；再保险行为对投资于股票的数量没有影响，而对投资于零息票债券的数量产生较大的影响. |
| 英文摘要 |
| Insurance company can purchase proportional reinsurance to hedge the risk of insurance. At the same time, insurance company can invest its wealth into the financial market to preserve or increase the value. In this paper, surplus process is supposed to be driven by Brownian motion with drift, short rate is described by stochastic affine interest rate model and the volatility of stock price is governed by Heston stochastic volatility model. By using the technique of stochastic dynamic programming and HJB equation, optimal reinsurance-investment strategy with exponential utility is obtained in explicit form. A numerical example is given to analyze the sensitivity of optimal reinsurance-investment strategy to model parameters. Research results display that optimal reinsurance strategy does not only depend on the parameters of insurance market, but also depends on the parameters of financial market；optimal reinsurance –investment strategies with stochastic interest rate and stochastic volatility are closely related to the dynamics of interest rate and have nothing to do with the dynamics of volatility；the reinsurance behavior has no effect on the amount in the stock, yet has a considerable influence on the amount in the zero-coupon bond. |